Zerothly, there are the watched. These can be defined as
those to whom the function "watches" can be applied,
returning the value "the watched". That is, they are self-
aware and may have lives which they themselves examine.

Firstly,
there are the watchers, for example the police,
intelligence services, professional bodies, OFSTED or the
CRB - in general, certain quangos, the government, local
government and various other things such as security
firms. They are people or organisations to which the
function "watches" returns a different value than its
original. The watchers watch the watched rather than
themselves. Their function is to "surveill" the activities of
the watched.

Secondly, there are organisations or people who are
concerned about "who watches the watchmen". These
people include pressure groups, charities, concerned
individuals, possibly also certain MPs and so on. These
watch the watchmen, so the function "watches" returns a
different value again, but that value can again return a
different value when the function "watches" is applied to
it. Specific examples would be the NSPCC, Greenpeace,
TICL (back when it existed) and umbrella professional
associations such as exist in the EU.

Thirdly, there are more people who are concerned about
the activities of such organisations and people. For
instance, there are those who feel that Greenpeace or the
NSPCC have reached a stage where they promote their
existence by interpreting what goes on on the level below
them in a certain manner. Once again, the function
"watches" returns a different value, which in turn returns
another until we finally reach "the watched".

Fourthly, there are at least people if not organisations who
observe the behaviour of those who are suspicious of such
organisations and become concerned about their paranoia.
These people constitute a group to whom the function
"watch" can be applied yet again.

I'm not sure how many times this process can be iterated,
but looking at it this way it becomes rather familiar.
These are very similar to Church numerals. At the bottom
there are the rather appropriately named "zeroes" - those
who don't matter, have no value in the system and are
simply watched. They don't watch anything, except maybe
television. Above them are a series of cardinal numerals
which behave in a more Orwellian or "Report On Probability
A" manner. These have value in the system. Hence the
Lambda Calculus can be applied to this system.

That means, moreover, that arithmetic can be done within
this system. Peano's axioms apply. Any organisation or
person within this system has the same value as itself, and
derives its value from how many levels of watching are
going on. That's a reflexive property. If it has the same
value, i.e. is on the same level, as another organisation, it
is equal to it and the other is equal to it too. If it's equal
to another organisation in that respect, and that
organisation is equal to a third, the first organisation is
also equal to the third - transitivity. Any organisation or
person which is equal to something is a member of this
system. Therefore, this is a system in which addition and
multiplication can be done. Effectively, there is an
arithmetic, within limits, which can be performed in the
system of organised suspicion of others.

This also means there are theoretical entities within this
system. For instance, there are infinitely suspicious
organisations or individuals who watch everything, even
themselves. Maybe there are even uncountably infinitely
suspicious such entities.

Questions:

Are there organisations who watch themselves? Is there
an organisation which only watches organisations which do
not watch themselves? Does that organisation watch
itself? Does there need to be another way of describing
the calculus of suspicion which can avoid this paradox?

Could there be organisations with negative or non-integral
levels of suspicion?

Is there a way of dividing or subtracting levels of
suspicion?

Should we establish a series of organisations which are so
unwatching that even watching them doesn't lead to them
actually being watched? Is it possible that such
organisations already exist in an undiscovered and maybe
even undiscoverable form? Should we be suspicious of
these organisations, or would that be dangerous because
they would absorb all our suspicions and lead to us not
being suspicious enough and thereby susceptible to the
likes of spam or being accused of crimes we not only have
not committed but cannot commit? On the other hand, could we perhaps bribe such organisations to do things for us by having them pay us?

What should we do about these dangerously non-suspicious
entities? They are unfindable. I find that thought very
frightening indeed, if indeed it is a thought.

No, don't think so. Take a spy. Their job is to spy
on others, so to simplify it the function of
watching is applied simply to at least one object
outside the set of spies of which that spy is a
member, and probably to another set of spies too.
That applies to the set of spies in, for example,
MI6 or the CIA too. They may also spy on their
own spies, but in that case there is a set which
includes spies who spy on other spies, who are in
the set of spies who do not spy on their own
spies. You can count members of those sets
separately as separate sets because they are "CIA
spies considered in their role as spies on other
spies who are not members of the CIA" or "CIA
spies considered in their role as spies on other
spies which are members of the CIA". However,
that does mean that the roles are what are being
counted rather than either organisations or
individuals. Thanks for helping me to get to that
realisation.

That means you could watch yourself a la 'A
Scanner Darkly' and still be counted as a spy to
whom the concept "Custodeo custodem" applies -
"I watch a watchman" - but you are also both a
watched person and a simple, first-order
custodian. So you have three personas.

It isn't necessarily the case that this recurses to
infinity, there are for example, only 5 platonic solids
- and there may well be be some deep limiting
analogy between the number of faces and vertices
that an object can be constructed from that also
applies to the network of
watched/watcher/ suspicion/suspect that you
describe.

Since we ourselves are 'In' an 'Organisation' (The Halfbakery), what value would the function return from the argument 'The group of us who have read this and have now become intrigued, thereby having become concerned about entities who watch other organisations who watch the zerothly watched'?

And is there therefore a possibility that those who read this actual annotation, as written by me, return a recursive value?

What truly makes us human is our ability to learn behavior from others' craft. Paranoia (fear without memes) is another uniquely human functionality arising, as a matter of course, in response to conspiracies of secrecy. Governments have power according to value derived from caches of secrets. All sort of conspiratorial edginess occurs across the continuum from originality to awe; so, why not quantify it? Vicis verto buns.

Social control of the inner man is labeled "acceptance", it is the only external locus of control that is considered status quo. That's why narcissists, on par with borderlines, are the most tumultuous among disordered personality types, and nihilists the least popular.

An interesting conjecture that the absence of watchfulness places one outside suspicion, unfindable. That may or may not be true of a nihilist; and, might be achieved by way of the 'false positive' atmosphere around some antisocial types wherein they'd find a place to be calm amid the chaos.

Combining lambda calculus with _Report from
Probability A_ is certainly my cup of tea, but does
the idea really hold water? Specifically, recursion
seems the wrong concept here; the branch of
math(s) that seems most applicable would be
graph theory. And applying graph theory to social
networks is kind of old hat.

The fact that you *can* use recursion to describe
cyclic graphs doesn't mean it's the natural way to
do it. After all, tail recursion does the work of
iteration, and, more generally, lambda calculus
can do anything a Turing machine can.

The new element here might be that the nodes in
the graph (or network) are sets, and that some
node/sets may,
as you point out, be nondisjoint with each other.

It could be a set of asymmetrical functions
"watches(x,y)", where x is a role and y is a
perceived person, i.e. x is the adoption of the role
of the watcher, effectively a reduction of one's
full identity, and y is the person watched, but
that person is a similar reduction as constructed in
the mind of the watcher. So it's sort of
existentialist: both arguments are reductions of
the real blurring buzzing confusion of the manifold
to a couple of apparently concrete objects.
However, just because we're trying to force them
to become concrete doesn't mean we succeed. I
recognise that right this second, this annotation is
more a string than something which refers
successfully.

[Mouseposture], i suppose i see that as a question
of whether this is pure or applied. I'll just have to
go away and think about what you've said because
right now i can't answer that. A brief and possibly
futile flight of fancy there is, since lambda calculus
is another way of looking at a Turing machine, can
there be hypercomputers which apply to
hierarchies of suspicion? And would it get anyone
anywhere if there could?

I have no problem with the pointlessness of the musing; it's the relative incoherence (by [nineteenthly]'s normally high standards) which troubles me. Indoors or out, I hope you're all right, [nineteenthly]. Maybe you could prescribe yourself some sort of herbal pick-me-up.

No, it's fine. I think the problem is i've spent too long on here recently and
need to do other stuff for a bit. Currently trying to get my head round
functional programming for [eleventeenthly]'s benefit and this is a kind of kick-
around with the notion to see how much sense i can make. I've forgotten a lot
of stuff about the lambda calculus and i'm trying to see if i can say something
coherent with it.